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2 years ago

What is this answer? I have no idea. pls help :( will give brainliest

Mathematics

1 answer:

Artist 52 [7]2 years ago

5 0

The answer is B.

Negative numbers are to the far left if you were using a number line, so -1 to the 3rd power is -1. Everything else is positive. 1/4 is the same as 0.25 which is less than positive 1, positive 8.8 is next and the last would be -5 to the 2nd power which is 25.

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How many sets of three consecutive integers are there in which the sum of the three integers equals their product?

skad [1K]

Answer:

Step-by-step explanation:

since the 3 integers are consecutive, we are dealing with x, x+1, x+2.

and their sum is the same as their product :

x + (x + 1) + (x + 2) = x(x + 1)(x + 2)

3x + 3 = x(x² + 3x + 2) = x³ + 3x² + 2x

x³ + 3x² - x - 3 = 0

this is a polynomial of third degree.

and as such it has 3 solutions.

of course, it could be that some of them are the same or are even in the realm of complex numbers (i = sqrt(-1)), but usually these 3 solutions are different real numbers.

I tried x=1 just to see, and, hey, it is a solution for this equation.

x = 1 means that the other 2 consecutive integers are 2 and 3.

and indeed, 1+2+3 = 1×2×3 = 6.

now it is easier to find the other 2 solutions, as a zero solution can be expressed as a factor of the whole expression.

for x = 1 the factor term is (x - 1), as this term is then turning 0, when x = 1.

I can divide the main expression by this factor and then analyze the quotient about the other 2 solutions.

x³ + 3x² - x - 3 : x - 1 = x² + 4x + 3

- x³ - x²

----------------

0 4x² - x

- 4x² - 4x

-----------------------

0 + 3x - 3

- 3x - 3

---------------------------

0 0

so, the original expression can be written as

(x² + 4x + 3)(x - 1).

now we need to find the 2 zero solutions for x²+4x+3

the general solution to a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

a = 1

b = 4

c = 3

so,

x = (-4 ± sqrt(4² - 4×1×3))/(2×1) =

= (-4 ± sqrt(16 - 12))/2 = (-4 ± sqrt(4))/2 =

= (-4 ± 2)/2 = -2 ± 1

x1 = -2 + 1 = -1

x2 = -2 - 1 = -3

so, we have the additional solutions :

-1 0 1

-3 -2 -1

-1 + 0 + 1 = -1×0×1 = 0

-3 + -2 + -1 = -3×-2×-1 = -6

and there we have it fully proven :

there are 3 different sets of 3 consecutive integers with the same sum as product.

4 0

2 years ago

Which shows rotational symmetry?

s344n2d4d5 [400]

It is actually the top one on the second picture because if you were to rotate it 180 degrees, it would end up on the same points

4 0

2 years ago

Read 2 more answers

What is 3p + 2 > -10

bezimeni [28]

Answer:

p> -4

Step-by-step explanation:

3p + 2 > -10

3p > -10 -2

p> -4

7 0

2 years ago

D’Quan’s grandmother made a quilt for his bed. The quilt is

damaskus [11]

One Square Meter= 10.764 Square Feet.
The total area of the quilt in meters is $4.465m^{2}$
As you're looking for square feet, you've then got to multiply this by 10.764
4.465*10.764= 48.06086 square feet.
Rounded, this is 48.06 square feet.
Hope this helps :)

7 0

2 years ago

Read 2 more answers

Maya drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 12 hours. When Maya drove

Roman55 [17]

Answer:

480 miles.

Step-by-step explanation:

Let x represent the distance between Maria's house and mountains ans r represent Maria's rate for going trip.

We have been given that there was heavy traffic on the way there, and the trip took 12 hours.

$\text{Distance}=\text{Rate}\times \text{Time}$

$x=12r$

We are also told that hen Maya drove home, there was no traffic and the trip only took 8 hours. Maria's average rate was 20 miles per hour faster on the trip home.

So Maria's speed while returning back would be $r+20$ .